树 2016.7.13

1、团队程序设计天梯赛-练习集-L2-006 树的遍历

解题思路：

利用后序遍历和中序遍历建树，再 bfs 求层级遍历

#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>#include <algorithm>#include <queue>#include <vector>#include <stack>#include <map>#include <cmath>#include <cctype>using namespace std;typedef long long ll;typedef unsigned long long ull;typedef unsigned int uint;const ull mod = 1e9 + 7;const int INF = 0x7fffffff;const int maxn = 30 + 10;int N;int Post[maxn], In[maxn];struct Tree {    int Left, Right;};Tree tree[100000];int Build(int Post_low, int Post_high, int In_low, int In_high);void bfs(void);int main(){#ifdef __AiR_H    freopen("in.txt", "r", stdin);#endif // __AiR_H    scanf("%d", &N);    for (int i = 0; i < N; ++i) {        scanf("%d", &Post[i]);    }    for (int i = 0; i < N; ++i) {        scanf("%d", &In[i]);    }    memset(tree, 0, sizeof(tree));    Build(0, N, 0, N);    bfs();    return 0;}int Build(int Post_low, int Post_high, int In_low, int In_high){    if (In_low+1 > In_high) {        return 0;    }    int root = Post[Post_high-1];    int Pos = In_low;    while (In[Pos] != root) {        ++Pos;    }    int Count = Pos - In_low;    tree[root].Left = Build(Post_low, Post_low+Count, In_low, Pos);    tree[root].Right = Build(Post_low+Count, Post_high-1, Pos+1, In_high);    return root;}void bfs(void){    queue<int> Queue;    Queue.push(Post[N-1]);    queue<int> ans;    while (!Queue.empty()) {        int t = Queue.front();        if (t == 0) {            break;        }        Queue.pop();        ans.push(t);        if (tree[t].Left != 0) {            Queue.push(tree[t].Left);        }        if (tree[t].Right != 0) {            Queue.push(tree[t].Right);        }    }    printf("%d", ans.front());    ans.pop();    while (!ans.empty()) {        printf(" %d", ans.front());        ans.pop();    }    printf("\n");}

2、团队程序设计天梯赛-练习集-L2-004 这是二叉搜索树吗？

#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>#include <algorithm>#include <queue>#include <vector>#include <stack>#include <map>#include <cmath>#include <cctype>using namespace std;typedef long long ll;typedef unsigned long long ull;typedef unsigned int uint;const ull mod = 1e9 + 7;const int INF = 0x7fffffff;const int maxn = 1e3 + 10;int BST[maxn];int N;int num = 0;bool Text(int Left, int Right, bool Is_Mirror);void Printf(int Left, int Right, bool Is_Mirror);int main(){#ifdef __AiR_H    freopen("in.txt", "r", stdin);#endif // __AiR_H    scanf("%d", &N);    for (int i = 0; i < N; ++i) {        scanf("%d", &BST[i]);    }    if (Text(0, N, 0)) {        printf("YES\n");        Printf(0, N, 0);        printf("\n");    } else if (Text(0, N, 1)) {        printf("YES\n");        Printf(0, N, 1);        printf("\n");    } else {        printf("NO\n");    }    return 0;}void Printf(int Left, int Right, bool Is_Mirror){    if (Left+1 > Right) {        return;    }    int root = BST[Left];    int Count = Left+1;    if (!Is_Mirror) {        while (Count < Right && BST[Count] < root) {            ++Count;        }    } else {        while (Count < Right && BST[Count] >= root) {            ++Count;        }    }    Printf(Left+1, Count, Is_Mirror);    Printf(Count, Right, Is_Mirror);    printf(++num  == 1 ? "%d" : " %d", root);}bool Text(int Left, int Right, bool Is_Mirror){    if (Left+1 >= Right) {        return true;    }    int root = BST[Left];    int Count = Left+1;    int Mid = Count;    if (!Is_Mirror) {        while (Count < Right && BST[Count] < root) {            ++Count;        }        Mid = Count;        while (Count < Right && BST[Count] >= root) {            ++Count;        }        if (Count != Right) {            return false;        }    } else {        while (Count < Right && BST[Count] >= root) {            ++Count;        }        Mid = Count;        while (Count < Right && BST[Count] < root) {            ++Count;        }        if (Count != Right) {            return false;        }    }    return (Text(Left+1, Mid, Is_Mirror) && Text(Mid, Right, Is_Mirror));}

3、团队程序设计天梯赛-练习集-L2-011 玩转二叉树

解题思路：

先利用中序遍历和前序遍历建镜像树，再 bfs 求层级遍历

#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>#include <algorithm>#include <queue>#include <vector>#include <stack>#include <map>#include <cmath>#include <cctype>using namespace std;typedef long long ll;typedef unsigned long long ull;typedef unsigned int uint;const ull mod = 1e9 + 7;const int INF = 0x7fffffff;const int maxn = 30 + 10;struct Tree {    int Left, Right;};Tree tree[100000];int N;int Pre[maxn], In[maxn];int Build(int Pre_low, int Pre_high, int In_low, int In_high);void bfs(void);int main(){#ifdef __AiR_H    freopen("in.txt", "r", stdin);#endif // __AiR_H    scanf("%d", &N);    for (int i = 0; i < N; ++i) {        scanf("%d", &In[i]);    }    for (int i = 0; i < N; ++i) {        scanf("%d", &Pre[i]);    }    memset(tree, 0, sizeof(tree));    Build(0, N, 0, N);    bfs();    return 0;}int Build(int Pre_low, int Pre_high, int In_low, int In_high){    if (In_low+1 > In_high) {        return 0;    }    int root = Pre[Pre_low];    int Pos = In_low;    while (In[Pos] != root) {        ++Pos;    }    int Count = Pos-In_low;    tree[root].Left = Build(Pre_low+1+Count, Pre_high, Pos+1, In_high);    tree[root].Right = Build(Pre_low+1, Pre_low+1+Count, In_low, Pos);    return root;}void bfs(void){    queue<int> Queue;    queue<int> ans;    Queue.push(Pre[0]);    while (!Queue.empty()) {        int t = Queue.front();        if (t == 0) {            break;        }        Queue.pop();        ans.push(t);        if (tree[t].Left != 0) {            Queue.push(tree[t].Left);        }        if (tree[t].Right != 0) {            Queue.push(tree[t].Right);        }    }    printf("%d", ans.front());    ans.pop();    while (!ans.empty()) {        printf(" %d", ans.front());        ans.pop();    }    printf("\n");}

4、Vijos 1114 FBI树

#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>#include <algorithm>#include <queue>#include <vector>#include <stack>#include <map>#include <cmath>#include <cctype>using namespace std;typedef long long ll;typedef unsigned long long ull;typedef unsigned int uint;const ull mod = 1e9 + 7;const int INF = 0x7fffffff;const int maxn = 1100;char s[maxn];int num[maxn];int N;void dfs(int low, int high);int main(){#ifdef __AiR_H    freopen("in.txt", "r", stdin);#endif // __AiR_H    scanf("%d%s", &N, s);    int len = strlen(s);    for (int i = 0; i < len; ++i) {        num[i] = s[i] - '0';    }    dfs(0, len-1);    printf("\n");    return 0;}void dfs(int low, int high){    if (low == high) {        if (num[low] == 1) {            printf("I");        } else {            printf("B");        }        return;    }    int mid = (low+high+1) >> 1;    dfs(low, mid-1);    dfs(mid, high);    bool have_0 = false, have_1 = false;    for (int i = low; i <= high; ++i) {        if (num[i] == 1) {            have_1 = true;        } else {            have_0 = true;        }        if (have_0 && have_1) {            break;        }    }    if (have_0 && have_1) {        printf("F");    } else if (have_0) {        printf("B");    } else {        printf("I");    }}

5、二叉树的遍历问题

描述

输入一棵二叉树的先序和中序遍历序列，输出其后序遍历序列。

输入

输入共两行，第一行一个字符串，表示树的先序遍历，第二行一个字符串，表示树的中序遍历。树的结点一律用小写字母表示。

输出

输出仅一行，表示树的后序遍历序列。

样例输入

abdecdbeac

样例输出

debca

#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>#include <algorithm>#include <queue>#include <vector>#include <stack>#include <map>#include <cmath>#include <cctype>using namespace std;#define DEBUG printf("DEBUG\n")typedef long long ll;typedef unsigned long long ull;typedef unsigned int uint;const ull mod = 1e9 + 7;const int INF = 0x7fffffff;const int maxn = 1e6 + 10;char Pre[maxn], In[maxn];struct Tree {    int Left, Right;};Tree tree[40];int Pre_len, In_len;bool vis[40];int Build(int Pre_low, int Pre_high, int In_low, int In_high);void Printf(int root);int main(){#ifdef __AiR_H    freopen("tree.in", "r", stdin);    freopen("tree.out", "w", stdout);#endif // __AiR_H    scanf("%s%s", Pre, In);    memset(tree, -1, sizeof(tree));    memset(vis, false, sizeof(vis));    Pre_len = strlen(Pre);    In_len = strlen(In);    Build(0, Pre_len, 0, In_len);    Printf(Pre[0] - 'a');    printf("\n");    return 0;}int Build(int Pre_low, int Pre_high, int In_low, int In_high){    if (In_low+1 > In_high) {        return -1;    }    int root = Pre[Pre_low] - 'a';    int Pos = In_low;    while ((In[Pos]-'a') != root) {        ++Pos;    }    int Count = Pos - In_low;    tree[root].Left = Build(Pre_low+1, Pre_low+1+Count, In_low, Pos);    tree[root].Right = Build(Pre_low+1+Count, Pre_high, Pos+1, In_high);    return root;}void Printf(int root){    if (root == -1) {        return;    }    Printf(tree[root].Left);    Printf(tree[root].Right);    printf("%c", root+'a');}